Costas Efthimiou is a University of Central Florida physics professor claims he has mathematic proof that the vampires--at least as they are depicted in legend--simply can't exist. The logic goes something like this:
"On Jan 1, 1600, the human population was 536,870,911. If the first vampire came into existence that day and bit one person a month, there would have been two vampires by Feb. 1, 1600. A month later there would have been four, and so on. In just two-and-a-half years the original human population would all have become vampires with nobody left to feed on."
Playing devil's..er...Dracula's advocate, here's where the 'proof' breaks down: Vampires can feed without turning the victim into a vampire. In most versions of the legend, there is some level of ritual involved--bitten three times, then fed the blood of the sire vampire, usually--that confers vampirism upon a victim. Otherwise, you're just a walking happy meal. So nice try, professor, but you're going to have to do better than that to prove that bloodsucking nosferatu are epidemeologically impossible.